Why, you may ask?
The Python sympy symbolic library provides solutions to single, linear Diophantine equations in terms of parametric variables. For instance,
{(t_0, -9*t_0 - 5*t_1 + 154, -5*t_0 - 3*t_1 + 77)}
Without worrying about coding details, how can one solve such a system of parametric expressions for values of the original variables constrained to be, for instance, greater than zero.
Are there any opensource products?